The present invention relates to thermographic nondestructive testing techniques for determining the thickness of an object. More particularly, the present invention relates to a infrared transient thermography method for analyzing stacks of thermal data image-frames that employs a Fast-Fourier Transform thermal resonance function to determine thickness.
Over the years, various nondestructive ultrasonic measurement techniques have been utilized to determine cross-sectional thickness of cast metal and other solid objects. Conventionally, the object is probed with ultrasonic waves which penetrate the surface and are reflected internally at the opposite side or surface of the object. Based upon the time required to receive a reflected wave, the distance to the opposite (back) side can be determinedxe2x80x94giving the thickness of the object at that point. Unfortunately, conducting ultrasonic measurements of this sort to examine the cross-sectional thickness for most of an object would usually necessitate a cumbersome and time-consuming mechanical scanning of the entire surface with a transducer. In addition, to facilitate intimate sonic contact between the transducer and the object surface, a stream of liquid couplant must be applied to the surface or, alternatively, total immersion of the object in the couplant must be accommodated. Such accommodations, however, are most often not very practical or even feasible for numerous structural and material reasons. For example, ultrasonic systems capable of scanning and analyzing geometrically complex parts are typically very expensive and complicated. In addition, a mechanical scanning of the transducer over the surface of a large object can literally take hours.
Moreover, when conducting ultrasonic measurements on certain metal objects, the internal crystal orientation and structure of the metal can cause undesirable noise and directional effects that contribute to inaccuracies in the acquired data. This inherent limitation of ultrasonic measurements proves to be a serious drawback when testing components constructed of crystalline or xe2x80x9cdirectionalxe2x80x9d metals such as often used in contemporary turbine airfoils.
In contrast, infrared (IR) transient thermography is a somewhat more versatile nondestructive testing technique that relies upon temporal measurements of heat transference through an object to provide information concerning the structure and integrity of the object. Since heat flow through an object is substantially unaffected by the micro-structure and the single-crystal orientations of the material of the object, an infrared transient thermography analysis is essentially free of the limitations this creates for ultrasonic measurements. In contrast to most ultrasonic techniques, a transient thermographic analysis approach is not significantly hampered by the size, contour or shape of the object being tested and, moreover, can be accomplished ten to one-hundred times faster than most conventional ultrasonic methods if testing objects of large surface area.
One known contemporary application of transient thermography, which provides the ability to determine the size and xe2x80x9crelativexe2x80x9d location (depth) of flaws within solid non-metal composites, is revealed in U. S. Pat. No. 5,711,603 to Ringermacher et al., entitled xe2x80x9cNondestructive Testing: Transient Depth Thermographyxe2x80x9d; and is incorporated herein by reference. Basically, this technique involves heating the surface of an object of interest and recording the temperature changes over time of very small regions or xe2x80x9cresolution elementsxe2x80x9d on the surface of the object. These surface temperature changes are related to characteristic dynamics of heat flow through the object, which is affected by the presence of flaws. Accordingly, the size and a value indicative of a xe2x80x9crelativexe2x80x9d depth of a flaw (i.e., relative to other flaws within the object) can be determined based upon a careful analysis of the temperature changes occurring at each resolution element over the surface of the object. Although not explicitly disclosed in the above referenced Ringermacher patent, the xe2x80x9cactualxe2x80x9d depth of a flaw (i.e., the depth of a flaw from the surface of the object) can not be determined unless a xe2x80x9cstandards blockxe2x80x9d, having voids at known depths, or a thermally thick (xe2x80x9cinfinite half-spacexe2x80x9d) reference region on the object is included as part of the thermographic data acquisition and analysis for comparison against the relative depth values.
To obtain accurate thermal measurements using transient thermography, the surface of an object must be heated to a particular temperature in a sufficiently short period of time so as to preclude any significant heating of the remainder of the object. Depending on the thickness and material characteristics of the object under test, a quartz lamp or a high intensity flash-lamp is conventionally used to generate a heat pulse of the proper magnitude and duration. However, the specific mechanism used to heat the object surface could be any means capable of quickly heating the surface to a temperature sufficient to permit thermographic monitoringxe2x80x94such as, for example, pulsed laser light. Once the surface of the object is heated, a graphic record of thermal changes over the surface is acquired and analyzed.
Conventionally, an infrared (IR) video camera has been used to record and store successive thermal images (frames) of an object surface after heating it. Each video image is composed of a fixed number of pixels. In this context, a pixel is a small picture element in an image array or frame which corresponds to a rectangular area, called a xe2x80x9cresolution elementxe2x80x9d, on the surface of the object being imaged. Since, the temperature at each resolution element is directly related to the intensity of the corresponding pixel, temperature changes at each resolution element on the object surface can be analyzed in terms of changes in pixel contrast. The stored IR video images are used to determine the contrast of each pixel in an image frame by subtracting the mean pixel intensity for a particular image frame, representing a known point in time, from the individual pixel intensity at that same point in time.
The contrast data for each pixel is then analyzed in the time domain (i.e., over many image frames) to identify the time of occurrence of an xe2x80x9cinflection pointxe2x80x9d of the contrast curve data, which is mathematically related to a relative depth of a flaw within the object. Basically, as applied to an exemplary xe2x80x9cplate-likexe2x80x9d object of consistent material and thickness L, a migrating heat-flux pulse impinging on an object takes a certain xe2x80x9ccharacteristic timexe2x80x9d, TC, to penetrate through the object to the opposite side (back wall) and return to the front surface being imaged. This characteristic time, TC, is related to the thickness of the object, given the thermal diffusivity of the material, by the following equation:
TC=4L2/xcfx802xcex1xe2x80x83xe2x80x83EQU. 1
where L is the thickness (cm) of the object and xcex1 is the thermal diffusivity (cm2/sec) of the material. (An object may also be thermally imaged from a side of the object opposite the heat-flux source. This merely results in a value of TC being different by a factor of four.)
From empirical observations it is known that after a heat pulse impinges on a plate-like object, the surface temperature observed from the same side of the object (i.e., the front) rises in a fashion that is also dependent on the thickness and the thermal diffusivity of the material. Moreover, from a graph of the temperature vs. time (T-t) history of the surface, one can determine the characteristic time, TC, in terms of a unique point on the T-t curve, called the xe2x80x9cinflection point.xe2x80x9d This inflection point, tinfl, is indicated by the point of maximum slope on the T-t curve (i.e., peak-slope time) and is related to the characteristic time, TC, by the following equation:
tinfl=0.9055 TCxe2x80x83xe2x80x83EQU. 2
This relationship between the inflection point and the characteristic time, as expressed by EQU. 2 above, is precise to approximately 1% for one-dimensional (1-D), as well as two-dimensional (2-D), heat flow analysis. Once an inflection point, tinfl, is determined from the T-t response, a relative thickness, L, of the object can be determined from EQU. 1 using the known thermal diffusivity, xcex1, of the material and the actual value of TC from EQU. 2.
In this regard, a more detailed discussion of the heat-flow invariant relationship between the peak-slope time (inflection point) and the material xe2x80x9ccharacteristic timexe2x80x9d as defined above may be found in the Review Of Progress In Quantitative Nondestructive Evaluation, in an article by Ringermacher et al., entitled xe2x80x9cTowards A Flat-Bottom Hole Standard For Thermal Imagingxe2x80x9d, published May 1998 by Plenum Press, New York, which is incorporated herein by reference.
Unfortunately, the above mentioned apparatus and method of U.S. Pat. No. 5,711,603 to Ringermacher et al. only produces xe2x80x9crelativexe2x80x9d depth measurements. It can not be used to obtain a quantitative value for the actual thickness of a metal object at a desired point. Consequently, an improved method of conducting IR transient thermography and processing the acquired data which would permit a determination of the actual thickness of metal objects was needed. One such method and apparatus is disclosed in a commonly assigned co-pending U.S. patent application (Ser. No. 09/292,886) of Ringermacher et al. filed Apr. 4, 1999. Basically, the arrangement disclosed therein utilizes a focal-plane array camera for IR image data acquisition and high-power flash lamps to rapidly heat the surface of a desired examined object along with a slab standard reference object composed of similar material and having portions of known thickness (a xe2x80x9cthermally thickxe2x80x9d section of the examined object may optionally be used as an xe2x80x9cinfinite half-spacexe2x80x9d thermal reference). The flash-lamp are fitted with spectrally tuned optical filters that minimize long-wave IR xe2x80x9cafterglowxe2x80x9d emissions and reduce background radiation effects which affect the accuracy of thermal measurements. A predetermined number of IR image frames are acquired and recorded over a predetermined period of time after firing the flash-lamps to develop a temperature-time (T-t) history of the object surface (and the reference standard). Contrast versus-time data is then developed for each pixel in the image to determine object thickness at a location corresponding to the pixel position.
In the above described method, contrast-time data is developed by subtracting temperature-time data of the slab reference standard (or temperature-time data of a thermally thick xe2x80x9cdeepxe2x80x9d reference region of the object) from the temperature-time data of each pixel. Unfortunately, this method suffers from the disadvantage that it may introduce some degree of error when imaging objects that have varying surface uniformity. Moreover, it requires the presence of a slab standard in the image or the use of temperature-time data from a deep reference region on the objectxe2x80x94assuming such a reference region is available. In addition, a special coating must usually be applied to the surface of the object (and the slab standard) prior to IR imaging to enhance optical absorption and improve surface uniformity.
The present invention relates to a nondestructive testing method and apparatus for determining and displaying the actual thickness of an object through the use of high speed infrared (IR) transient thermography. An improved high-speed IR transient thermography analysis approach is utilized to accurately measure the thickness of an object and provide a visual coded display indicative of its cross-sectional thickness over a desired area of the object. A salient feature of this improved approach is the use of a Fast-Fourier Transform resonance function to determine thickness. One beneficial aspect is that the transient thermography method of the present invention does not require the presence of a reference slab standard in the image or a usable reference region on the examined object. In addition, there is no need for special surface preparations or special surface coatings to enhance optical absorption or improve surface uniformity of the object being examined.
Basically, the present invention provides a method and apparatus for analyzing the Real and Imaginary components of the Fast Fourier Transform (FFT) of a temperature-versus-time (T-t) response curve of a rapidly heated object to obtain a frequency value that is directly related to the particular characteristic time, TC, of transit for a thermal pulse through the object. Once the characteristic time is known, it can be used to compute a quantitative value for the thickness, L, between two surfaces of the object at a desired point according to EQU. 1 above. The T-t response is initially determined from thermal data acquired from successive IR camera image frames over a predetermined observation periodxe2x80x94preferably obtained from same-side (xe2x80x9cfront-sidexe2x80x9d) observations of the object. (Ideally, this observation period is at least somewhat longer than an anticipated characteristic time as determined from EQU. 1 above and an estimation of the thickness of the object being evaluated).
Essentially, the acquired thermal data is assembled to form an individual T-t response curve for each pixel in the image. The T-t response curve data associated with each pixel is then normalized and a Fast Fourier Transform (FFT) is performed to convert the data to the frequency domain. The Real component (or alternatively the Imaginary component) of the complex FFT is then analyzed to locate the inflection point of the T-t response in the frequency domain. The frequency value at this inflection point is related to the thermal characteristic time, TC, according to the relationships given by EQU. 3 and EQU. 4 below:
TCfRe=0.372xe2x80x83xe2x80x83EQU. 3
TCflm=0.748xe2x80x83xe2x80x83EQU. 4
where fRe is the Real component of the Fast Fourier Transform at the inflection point, and flm is the Imaginary component of the Fast Fourier Transform at the inflection point, of the T-t response data associated with each pixel.
The Real component of the FFT of the T-t response data is a xe2x80x9cresonance functionxe2x80x9dxe2x80x94operating much like a xe2x80x9cthermal absorptionxe2x80x9d function in the frequency domainxe2x80x94whose frequency half-width at the inflection point is directly related to the characteristic time, TC. Similarly, the Imaginary component of the FFT of the T-t response data is a xe2x80x9cpeaked functionxe2x80x9dxe2x80x94operating much like a xe2x80x9cthermal dispersionxe2x80x9d function in the frequency domainxe2x80x94whose frequency peak, flm, is also directly related to the characteristic time, TC. Accordingly, the location of the inflection point in the frequency domain, and hence determination of the characteristic time, is accomplished either by identifying the peak of the derivative function of the Real component of the FFT or by identifying the peak value of the Imaginary component of the FFT.
As illustrated in FIG. 1, the apparatus of the present invention includes an imaging system comprising one or more high power flash lamps fitted with special optical filters, an IR sensitive focal-plane array camera for data acquisition and a display monitor. A computer system controls the imaging system, records and analyzes surface temperature data acquired via the IR camera and provides a color or gray pattern-keyed image on the display monitor that accurately corresponds to thickness of the object.
The acquisition of surface temperature data is initiated by firing the flash-lamps to illuminate the surface of the object. Spectrally tuned optical filters are used to absorb and/or reflect all 3-5 micron IR radiation back into the flash-lamp(s). This prevents undesirable long-wave IR xe2x80x9cafterglowxe2x80x9d emissionsxe2x80x94typically generated by overheated metallic elements in the flash-lamps after the lamps are extinguishedxe2x80x94from reaching the object or the camera.
A predetermined number of image frames are then recorded over a period of time after the flash lamps are fired. Each recorded image frame being made up of a predetermined nxc3x97m array of image pixels whose intensity correlate to the surface temperature of the object at the time the frame data was acquiredxe2x80x94each pixel having an (x,y) location designation within the image frame that corresponds to a particular resolution element. The recorded IR image data is then used to develop the temperature-time (T-t) history for every elemental region or xe2x80x9cresolution elementxe2x80x9d over the region of interest on the object surface. Next, a xe2x80x9ckneexe2x80x9d point is identified in the characteristic curve formed by the historical T-t data for each of the pixels. To normalize the data for all the pixels, the T-t data curve is clipped and constant-padded just past this to produce a continuous xe2x80x9cflatxe2x80x9d curve portion of constant temperature value equal to the curve value at the clip point.
A mathematical derivative curve of the Real component of the FFT is then computed to identify the inflection point, fRe, of the T-t response data in the frequency domain. The derivative curve may be accurately computed, for example, by using a three-point data sampling having a first and third sample point separation that is proportionally related to the value of the image frame-number at the second sample point. Preferably, all local xe2x80x9cpeaksxe2x80x9d in the derivative computation are identified and filtered. (For example, a weighting function can be used to adjust the significance of any such localized peaks to best identify the actual inflection point frequency). Finally, the characteristic time, TC, and thickness, L, of the object at a location corresponding to each pixel is quantitatively determined according to EQU 1 and EQU 3.
Alternatively, the peak in the imaginary component of the FFT can be used to identify the inflection point, flm, of the T-t response data in the frequency domain. In this case, the peak can be readily determined by any conventional computational method. The characteristic time, TC, and thickness, L, of the object at a location corresponding to each pixel is then quantitatively determined according to EQU 1 and EQU 4.